Question

A truck weighing 50 kg changes its speed from $10m{s}^{-1}$ to $40m{s}^{-1}$ in 2 minutes. Find the power of its engine.

• A. 625 W
• B. 312.5 W
• C. 1250 W
• D. 937.5 W

Answer 1

The correct option is B

312.5 W

Mass of the truck, m = 50 kg
Initial speed, u = $10m{s}^{-1}$
Final speed, v = $40m{s}^{-1}$
Time taken, t = 2 minutes = $2\times 60=120s$
We know that Kinetic energy = $\frac{m{v}^2}{2}$
Initial kinetic energy = $\frac{m{u}^2}{2}=\frac{5\times 10\times 10}{2}$= 2500 J
Final kinetic energy =$\frac{m{v}^2}{2}=\frac{5\times 40\times 40}{2}$ = 40,000 J
Change in kinetic energy = 40000 J - 2500 J= 37500 J
Power of the engine = rate of change of energy = $\frac{changeinenergy}{timetaken}=\frac{37500}{120}$ = 312.5 W